Subgroups — C₂×C₁₁²×ΓL(1,𝔽₃₂) #49175993

Order 37510.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁²×ΓL(1,𝔽₃₂)	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₁₁²×C₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁²×C₃₁	C₂×C₅	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁×ΓL(1,𝔽₃₂)	C₁₁	1	12	yes	maximal, direct product factor
5	C₁₁×ΓL(1,𝔽₃₂)	C₂×C₁₁	1	12	yes	direct product factor
6	C₂×C₅×C₁₁²	—	31	1	no	maximal, Hall
7	C₂×C₁₁×C₃₁	C₅×C₁₁	1	12	yes	complemented
8	C₅×C₁₁²	—	31	1	no	Hall
9	C₁₁×C₃₁	C₂×C₅×C₁₁	1	12	yes	complemented
10	C₂×ΓL(1,𝔽₃₂)	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₁₁²	ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Hall
12	ΓL(1,𝔽₃₂)	C₂×C₁₁²	1	1	yes	characteristic, direct product factor, Hall
13	C₁₁²	C₂×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Sylow
14	C₂×C₅×C₁₁	—	31	12	no	—
15	C₂×C₃₁	C₅×C₁₁²	1	1	yes	characteristic, complemented, Hall
16	C₅×C₁₁	—	31	12	no	—
17	C₃₁	C₂×C₅×C₁₁²	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₁₁	C₁₁×ΓL(1,𝔽₃₂)	1	12	yes	direct product factor
19	C₁₁	C₂×C₁₁×ΓL(1,𝔽₃₂)	1	12	yes	direct product factor
20	C₂×C₅	—	31	1	no	Hall
21	C₅	—	31	1	no	Sylow
22	C₂	C₁₁²×ΓL(1,𝔽₃₂)	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₁₁²	ΓL(1,𝔽₃₂)
commutator, cosocle, hypocenter	C₃₁	C₂×C₅×C₁₁²
Frattini	C₁	G
Fitting, socle	C₂×C₁₁²×C₃₁	C₅
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₁₁²

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.